theydidthemath

probability of getting any particular combination of four random numbers in this range is (1/8)4 = 0.024%

edit: there's a lot of discussion about the random number generator in a ti-84. for your perusal, here is somebody who dug up the paper describing the method used (and verified it through emulation!), which is called a linear congruential random number generator. (actually this specific implementation appears to feed the output of one such generator into another, i think mostly to extend the period.) here is a direct link to that paper (implementation in figure 3). apparently the most common random number generators today are called 'mersenne twister' random number generators. the paper says the linear congruential random number generator used in the ti-83 has a period of 2.30484 * 1018 which is approximately 261 , whereas the most common mersenne twister implementation has a period of 219937 - 1. meaning that values will repeat each other every 261 times you use the random number generator on a ti-83. unless they're seeded with the same value at the factory, which many have suggested and would make me kinda sad.

A lot of these calculators have a seeded "random" number generator. It is pseudo-random and if you cleared the memory (reset the devoce) it would probably do it again

I don't have a definitive answer and it is late here, so sorry if that trails off.

Given the Amazon description, I'd say you need to place this somewhere between an Arduino and a Raspberry Pi, with the first not being able to run Doom and the second being able to do run it. Given that this came out in 2008, I'd say it is closer to an Arduino.

But there is actually a short story showing what it looks like from inside. That doesn't go into details of the used chip, but we can see there that a button cell is used to power that thing, something that isn't exactly used to power "powerful" stuff. The bigger ones hold up to 620mAh, which is nice, but have a maximum discharge current of ~0.2mA...which is...well, not a lot at all. From what I gather, that is hardly enough to run a very small variant of the Arduino. Which means that whatever is in there is actually not a general purpose chip, but the logic directly baked into circuits.

Which makes it rather unsuitable for running anything besides the logic it was designed for, unfortunately.

Arduino

Arduino is an open source computer hardware and software company, project, and user community that designs and manufactures single-board microcontrollers and microcontroller kits for building digital devices and interactive objects that can sense and control objects in the physical world. The project's products are distributed as open-source hardware and software, which are licensed under the GNU Lesser General Public License (LGPL) or the GNU General Public License (GPL), permitting the manufacture of Arduino boards and software distribution by anyone. Arduino boards are available commercially in preassembled form, or as do-it-yourself kits.

Arduino board designs use a variety of microprocessors and controllers.

Raspberry Pi

The Raspberry Pi is a series of small single-board computers developed in the United Kingdom by the Raspberry Pi Foundation to promote the teaching of basic computer science in schools and in developing countries. The original model became far more popular than anticipated, selling outside of its target market for uses such as robotics. Peripherals (including keyboards, mice and cases) are not included with the Raspberry Pi. Some accessories however have been included in several official and unofficial bundles.

Button cell

A watch battery or button cell is a small single cell battery shaped as a squat cylinder typically 5 to 25 mm in diameter and 1 to 6 mm high—like a button on a garment, hence the name. A metal can forms the bottom body and positive terminal of the cell. The insulated top cap is the negative terminal.

I couldn't find the actual specifications of a Cube World Cube. However, I think that Tamagochis will have fairly similar processing power to the Cube. But... I couldn't find the exact specifications of a Tamagochi either. What I did find however, is that they use a 4-bit microprocessor. A quick Google search led me to a PDF outlining the specifications of an EM6607 4-bit microprocessor, and so I am going to assume that the microprocessor has the same specifications and processing power as a cube. Let's do the math:

I'll start with the processor. Doom requires a single core processor running at 66Mhz to run. The Cube's processor runs at 32,768Hz. 66,000/32,768=2.01416016, but we'll round it up to 3, so we need 3 cubes minimum to have a fast enough processor to run Doom.

Now let's do the storage. Doom requires 40MB of ROM to install it. Were just going to assume that we don't need to install an operating system or a launcher, but that doom will launch when the cubes are turned on. Each cube has 32KB (2Kx16) of ROM. This means we need 40,000/32=1250 cubes minimum just to store the game. Let's move on to RAM.

The game requires 8MB of RAM, and each cube has 384 Bytes of RAM. 8,000,000/384=20833.3, but we'll round it to 20834 cubes. This is the new minimum amount of cubes so we have enough RAM for the game.

So assuming the cubes use the microprocessor I found online, we need a minimum of 20,834 cubes to run Doom. Whilst I was looking it up, I saw the average price for one cube was about £20 (~$26). To buy that many cubes, it would cost 20,834x20=£41,668 or $55,043. Hope this answers you question well OP.

Edit: There are 66MHz is 66,000,000Hz, not 66,000Hz. It's not 3 cubes to have enough processing power, it's 2015. Thanks u/ray_dog for pointing it out for me.

Edit 2: I forgot to multiply by 20, and just did it by 2 when working out the cost, so it would actually cost £416,680/$550,430.

Hi Math Friends! My kiddo gets math homework each night, and it's usually normal 2nd grade stuff. One of the problems tonight seems unusually broad. While I think it's a mistake of the wording of the problem, I am curious what the actual answer is (well, I am curious to know if I figured it out)

Or, in other terms, let d equal the number of darts thrown (assuming all hit the board), and let s equal the number of possible scores.

d * s = p will yield the result: Darts * scores = possibilities.

If d = 3 and s = 3, then p = 9.

You left off 2+2+2 (not sure if intentionally) but since it is the same as 4+1+1 it doesn't represent a different possible score. Interesting that there's 10 dart outcomes but only 9 score outcomes

Well, the problem did stipulate that all throws hit the board.

Public school math teacher here. This is not an awful problem. The idea is to get kids to do a bit of direct modeling (thus the little dart board), practice simple repeated addition (maybe as prep for multiplication, given the number choices), look for patterns (some cases lead to the same results), and practice meta-problem solving skills (like attention to detail and task focus). The direct modeling (drawing a bunch of little dart boards and trying different configurations of dots) is well within the abilities of a seven year old. Unfortunately, a lot of teachers will treat a problem like this as a throwaway -- give it a check or a 'good job' sticker and move on. It kind of deserves a bit of class discussion. Not a whole lesson, but give kids a chance to share their approaches -- kinda like what's happening in this thread!

According to this, the wind power of an average mature hurricane is 1.5 x 1012 W

This site gives an average of 100 W for a box fan. Let's assume an overall efficiency of 60% for the fan and motor so fans produce 60 W of usable air flow energy.

This gives up 2.5 x 1010 fans, or 25 billion fans. We'd need more if we used weak little desktop fans like the one pictured. Assuming of course that we can somehow magically get 100% of the fan energy to go directly towards getting rid of the hurricane.

Assuming the 25 trillion gallons of rainfall estimate is correct and a flow rate of 25 gallons per minute through a 3/4" hose at typical household pressure,

1 trillion minutes or
16.67 billion hours or
694 million days or
1.902 million years

In other words it would need to have been flowing since 100,000 years after the appearance of the first species in our genus, homo habilis.

Interesting addition:

According to the EPA's evaporation equation for pools, we could only achieve about 30,000 square feet of surface area before we reached equilibrium between the rate of water inflow and evaporation. This assumes 25 mph average winds, a 60 degree Fahrenheit surface temperature, and that my math and the equation are accurate for the system. The equation being accurate for such a system is extremely unlikely but it's still fun to speculate.

Not to mention the fact that it gets absorbed into the soil/rivers/streams.

It will also evaporate more rapidly as it's surface area grows, eventually hitting some kind of equilibrium

While /u/cnl219 has the theoretical lower bound correct, the real answer is never. A faucet of that size with that flow rate would never flood the area the size of the Houston metropolitan area due to natural hydrological processes and evaporation.

There's a fundamental flaw in the paper side because the paper industry maintains their own tree farms. They plant more than they cut down and maintain commercial forests that are healthier than natural ones with higher rates of photosynthesis. Using less paper is actually detrimental to tree conservation.

Are you fucking insane? That's about the same amount of calories it takes to walk half a mile.

There's so much wrong with this post I don't even know how to fully address it.

Obviously you aren't putting enough effort into your farts. They should leave you physically exhausted.

Farting doesn't burn any calories. When you fart, your muscles relax and you expel the gas. That's all that happens. Relaxing a muscle doesn't burn any calories, the gas itself doesn't take any calories with it when you fart.

Thus the chance of selecting 8 tiles and spelling DISASTER in order by first drawing/ejecting a D (4/100) then drawing an I (9/99), ... is 4*9*4*9*3*6*12*6/(100*99*98*97*96*95*94*93) which is 1679616/7503063898176000 ~ 2.2 x 10-10 or about 1 in 4.5 billion.

I'm also not concerned with orientation of the tiles (e.g., if the tile is either face-down, rotated 90 degrees/upside down). If I required them all to be oriented face up (50%) and not upside down (50% chance for non-symmetric tiles - e.g., except I or S, where they read the same upside down), then it would decrease the odds by a factor of (1/2)8 * (1/2)5 = 1/8192, to be about 1 in 36.6 trillion.

If we let a handful be 9 tiles and don't care about the first or last tile (e.g., ?DISASTER) works as well as (DISASTER?) for any tile ?, then we double the possibilities (e.g., from 1 in 4.5 billion to 1 in 2.23 billion).

Bravo.

The chance gets much higher if we don't care about the order ("could spell", not "spelt" or "spelled"). There are (8 choose 2)\6! = 20160 possible orderings, where (8 choose 2) takes care of the duplicate "s". Multiply your result by this value and we get 4.4*10-6 or 1 in 250,000. With a ninth letter, we get many more options, roughly a factor 10 more. Add the blank tile or a tenth letter and the chance begins to get realistic.

*Edit: Added alternative for people from the US.

Probably less, because these odds didn't factor in death from complications.

In a home with older toilets, an average flush uses about 3.6 gallons (13.6 liters), and the daily use is 18.8 gallons (71.2 liters) per person per day. In a home with ultra-low-flow (ULF) toilets, with an average flush volume of 1.6 gallons (6 liters), the daily use is 9.1 gallons (34.4 liters) per person per day.

So the usage is between 71 and 34 liters per day.

6 months is 180 days, timing the water usage with the time gives you anywhere between 12780 and 6120 l.